In [16], Sparse PCA (SPCA) is used to select signature OES variables. In [17], Partial Least Squares (PLS), support vector machines, and rules ensemble methods are compared with each other for process yield prediction. Dimensionality of the input data is reduced using PLS and rules ensemble within the prediction process.A general feature of these previous applications of dimension reduction of OES data is that generic methods (e.g., PCA, SPCA, or use of summary statistics) are applied directly to the full set of input wavelength variables, without regard to the specific nature of the dataset and these methods can have difficulty in finally isolating important variables in the original variable space. For example, it is not possible to trace back to individual wavelength measurements at a certain time point when only summary statistics are the output of the method [15].

In PCA-based methods, every Principal Component (PC) is a linear combination of all original variables. This is a problem if quantification of the contribution by each variable to certain PCs is required [18]. SPCA is a possible solution to this problem [19], but the grouping effect (equal weights tend to be given to highly correlated variables) is a weakness, leading to difficulty in final variable selection [16].Other general dimension-reduction methods also have disadvantages for direct application to the problem at hand. Ensemble methods have been shown to be successful in identifying important variables in the original space [20], however ensemble learning methods (e.g.

, boosting, bagging [21], rules ensembles [20]) need to be supervised by knowledge of output variables, which in our case would be actual etch-rate measurements, which are normally not available. Other supervised learning methods are similarly unsuitable in the current context. Factor Analysis (FA) [22], projection pursuit [23], Artificial Neural Networks (ANN), and Independent Component Analysis (ICA) all have their own particular issues. In [24], a number of problems are highlighted for the FA method, where it is often possible to extract too few or too many factors and factor stability can be a concern. For projection pursuit [23], high computational int
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